Circle Theorems Calculator

Circle Theorems Explorer

Explore the main circle theorems, and use the calculator modes where a numeric answer is meaningful.

Last updated: 2026-06-21T07:59:21.442Z

Angle at the Center

The angle subtended by an arc at the center is twice the angle subtended at the circumference.

Formula: Center angle = 2 × circumference angle

Enter a valid numeric angle in degrees.

Center angle

60°

Multiply the circumference angle by 2.

What are circle theorems?

Circle theorems are geometric rules that describe relationships between angles, arcs, chords, and tangents within a circle.

They let you work out unknown angles without direct measurement.

Key circle concepts

Chord

A line segment with both endpoints on the circle.

Tangent

A line that touches the circle at exactly one point.

Arc

A portion of the circumference between two points.

Segment

The region bounded by a chord and its arc.

Worked example

Find the center angle when the circumference angle is 35°.

Given: 35°

Rule: Center angle = 2 × circumference angle

Answer: 70°

Result

70°

Frequently asked questions

What is a cyclic quadrilateral?

A four-sided shape whose vertices all lie on one circle.

Does the calculator support every theorem numerically?

No. Some theorems are descriptive and do not produce a numeric output.

Why is the angle at the center double the circumference angle?

Because the center angle subtends the same arc but spans twice the angle.

Can I use decimals?

Yes. The calculator accepts numeric values, including decimals.

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